Connecting Young Star Clusters to CO Molecular Gas in NGC 7793 with ALMA-LEGUS

We present an investigation of the relationship between giant molecular cloud (GMC) properties and the associated stellar clusters in the nearby flocculent galaxy NGC 7793. We combine the star cluster catalog from the HST LEGUS (Legacy ExtraGalactic UV Survey) program with the 15 parsec resolution ALMA CO(2-1) observations. We find a strong spatial correlation between young star clusters and GMCs such that all clusters still associated with a GMC are younger than 11 Myr and display a median age of 2 Myr. The age distribution increases gradually as the cluster-GMC distance increases, with star clusters that are spatially unassociated with molecular gas exhibiting a median age of 7 Myr. Thus, star clusters are able to emerge from their natal clouds long before the timescale required for clouds to disperse. To investigate if the hierarchy observed in the stellar components is inherited from the GMCs, we quantify the amount of clustering in the spatial distributions of the components and find that the star clusters have a fractal dimension slope of $-0.35 \pm 0.03$, significantly more clustered than the molecular cloud hierarchy with slope of $-0.18 \pm 0.04$ over the range 40-800 pc. We find, however, that the spatial clustering becomes comparable in strength for GMCs and star clusters with slopes of $-0.44\pm0.03$ and $-0.45\pm0.06$ respectively, when we compare massive ($>$10$^5$ M$_{\odot}$) GMCs to massive and young star clusters. This shows that massive star clusters trace the same hierarchy as their parent GMCs, under the assumption that the star formation efficiency is a few percent.